CONFORMAL SCATTERING FOR A NONLINEAR WAVE EQUATION

Forced Vibrations for a Nonlinear Wave Equation

Regularity and Scattering for the Wave Equation with a Critical Nonlinear Damping

We show that the nonlinear wave equation u + ut = 0 is globally well-posed in radially symmetric Sobolev spaces Hk rad(R 3) × Hk−1 rad (R 3) for all integers k > 2. This partially extends the well-posedness in Hk(R3) × Hk−1(R3) for all k ∈ [1, 2], established by Lions and Strauss [12]. As a consequence we obtain the global existence of C∞ solutions with radial C∞ 0 data. The regularity problem ...

Volume integral equation formulation for scattering using conformal finite elements

A method of moments solution of volume integral eqna,tions (VTEs) for scattering and radiation problems involving arbitrarily shaped inhomogeneous dielectric structures is presented. The inhomogeneous region is modeled using second order hexahedral elements whereas low order conformal basis functions within these elements are used for the method of moments expansion of the unknown. The resultin...

Nonlinear wave evolution equation for critical layers.

Recent studies of the evolution of weakly nonlinear long waves in shear flows have revealed that when the wave field contains a critical layer, a new nonlinear wave equation is needed to describe the wave evolution. This equation is of the same type as the well-known Korteweg-de Vries equation but has a more complicated nonlinear structure. Our main interest is in the steady solitary wave solut...

Nonlinear progressive wave equation for stratified atmospheres.

The nonlinear progressive wave equation (NPE) [McDonald and Kuperman, J. Acoust. Soc. Am. 81, 1406-1417 (1987)] is expressed in a form to accommodate changes in the ambient atmospheric density, pressure, and sound speed as the time-stepping computational window moves along a path possibly traversing significant altitude differences (in pressure scale heights). The modification is accomplished b...